Mental Subtraction: Count Back or Count up

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1 Getting Started
2 Watch and Notice
3 Try It Together
4 Write It in Your Copy
5 Class Challenge
6 What Did We Notice?
7 What's Next
Pupil practice

1 - Getting Started ~4 mins

Here is a quick one to do in your head: what is 62 − 58? Hands up when you have it. Now the real question: when you worked it out, did you take 58 away from 62, or did you count up from 58 to 62 to find the gap?

Teacher Notes

Take three hands-up answers, not open call-outs. Then ask the second question and let two or three pupils describe their method out loud. Don't correct or rank the methods yet — the whole point of the lesson is that close numbers (62 and 58) make counting up the quick choice. So when the numbers are close together, counting up is faster.

👇 Mark your steps as done as you complete them.

+5 XP

2 - Watch and Notice ~9 mins

Two words for our jumps today: a back-jump is when we jump backwards to take an amount away, and a forward arc is when we jump forwards to count up the gap between two numbers. Both can reach the answer — we pick whichever is quicker.

75 − 6 by counting back

Are these numbers close or far apart? Watch the number line. We're only taking away a small amount — just 6 — so the quick way is one back-jump. We land on the answer.

71 − 68 by counting up

Are these numbers close or far apart? They are very close, so instead of taking away we use forward arcs from 68 up to 71. The arcs add up to the gap: +2 to 70, then +1 to 71, so the difference is 3.

84 − 30 by counting back

Are these numbers close or far apart? This is a tidy take-away: one big back-jump of 30 lands us straight on the answer.

92 − 47 by counting up

Are these numbers close or far apart? They are far apart, but forward arcs still work nicely if we step through a friendly number. We jump +3 from 47 up to 50, then +42 from 50 up to 92. Add the two arcs: 3 + 42 = 45, so the difference is 45.

Teacher Notes

Walk each example aloud, one at a time. The 'are these numbers close or far apart?' question is now on screen — read it out and take two hands-up answers before you reveal the jumps, so the watching class re-engages on each example.

75 − 6 — a small amount to take away: one back-jump. Say take away.
71 − 68 — very close: counting back would be slow, so count up. Say find the difference.
84 − 30 — a clean back-jump of 30.
92 − 47 — bridge through 50: +3 to 50, then +42 to 92; the two arcs (3 + 42) make 45.

The key idea to land: close numbers → count up; a small amount to take from a big number → count back.

👇 Mark your steps as done as you complete them.

+10 XP

3 - Try It Together ~11 mins

Today we work these through together on the hundred square: 53 − 8, then 67 − 64, then 80 − 35. For each one we decide first whether the two numbers are close or far apart, then show the count-back path or the count-up path across the rows. Watch what happens at a row boundary: for 53 − 8, counting back crosses from 53 down past 50, so we drop off the start of one row and carry on at the end of the row above. We say which path was shorter.

Count back or count up on the hundred square

Teacher Notes

This round is for talking it through together — pupils take turns at the board and the class agrees or corrects out loud.

For each subtraction, ask the class first: are these two numbers close together or far apart? Then send a pupil to show the path on the hundred square.

53 − 8 — a small amount to take away: count back. Point out the row-change as you cross from 53 down past 50 — the count keeps going, it just jumps up a row.
67 − 64 — very close: count up 64 → 67, only 3 steps.
80 − 35 — far apart: either count back 35 or count up from 35 to 80. Ask which felt shorter.

Revoice a strong answer: so because they were close, counting up only took three little steps.

+15 XP

4 - Write It in Your Copy ~2 mins

COPYBOOK MOMENT

In your maths copy, work these three subtractions. Beside each answer, write "took away" or "found the difference" to show how you did it.

75 − 6
63 − 59
80 − 35

Teacher Notes

Walk the room and glance at whether pupils picked the sensible method — close numbers like 63 and 59 should be "found the difference". This is whole-class copybook practice, not marking.

+10 XP

5 - Class Challenge ~8 mins

Today we work through these together on the number line: 45 − 7, then 52 − 48, then 83 − 36. For each one we add the jumps to reach the answer: back-jumps to take away, forward arcs to count up the difference. Before each one, decide whether the two numbers are far apart or close together.

Look carefully at 45 − 7: this is only a small amount to take away, so the quick way is to count back. Counting up from 7 all the way to 45 would be the slow way — don't fall for it.

Reach the answer with jumps

Teacher Notes

This round is the practice bank — pupils take turns at the board, check each answer, and the class confirms before moving on. Three problems in eight minutes gives each one a proper decide-then-solve-then-confirm cycle, so keep the board work brisk rather than over-explaining.

45 − 7 — a small amount to take away: count back, bridging through 40.
52 − 48 — very close: count up 48 → 52, just 4.
83 − 36 — far apart, count up cleanly: +4 to 40, then +43 to 83.

For each, ask the class first: far apart or close together? The 45 − 7 trap is now flagged on screen, so check pupils spotted it themselves.

+15 XP

Pupil practice

Module 2 · The Four Operations, Mental and Written Number

Lesson 14 · Mental Subtraction: Count Back or Count up

Download Activity Book page (PDF)

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Teacher Class Feed

1 - Getting Started ~4 mins

2 - Watch and Notice ~9 mins

75 − 6 by counting back

71 − 68 by counting up

84 − 30 by counting back

92 − 47 by counting up

3 - Try It Together ~11 mins

Count back or count up on the hundred square

4 - Write It in Your Copy ~2 mins

5 - Class Challenge ~8 mins

Reach the answer with jumps

Unlock the full learning experience

XP